F(x)=-1/2(x-2)^2-4
Graph the function

  see below

Step-by-step explanation:

The function is written in vertex form. It has a negative vertical scale factor, so you know ...

Vertex form is ...

  f(x) = a(x -h)^2 +k . . . . . . . . . . vertical scale factor "a", vertex (h, k)

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Since you know the vertex and scale factor, you can plot some points on the graph. I find it convenient to think in terms of units either side of the vertex. These are values of x that would make (x-2)^2 be 1^2, 2^2, 3^2, 4^2 and so on. The vertical scale factor of -1/2 tells you that the y-differences for these points will be -1/2, -4/2, -9/2, -16/2 from the vertex. Then we have ...

  vertex: (2, -4)

  1 unit either side of the vertex: (1, -4.5), (3, -4.5)

  2 units either side of the vertex: (0, -6), (4, -6)

  3 units either side of the vertex: (-1, -8.5), (5, -8.5)

  4 units either side of the vertex: (-2, -12), (6, -12)

You can plot these points and draw a smooth curve through them. Or, you can let a graphing calculator do it. The result will be similar to that shown below.

answer: 2x + 2 − 2 = 10 − 2; subtraction property of equality

step-by-step explanation:

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step-by-step explanation: